If the early returns prove accurate, the prime minister could be strengthened in dealings with Parliament before national elections to be held by next year. Mr. Maliki’s Dawa Party drew strong support in Basra and Baghdad, two of Iraq’s largest and most politically important provinces, according to political parties and election officials who spoke on the condition of anonymity because they were not authorized to discuss preliminary tallies.

The relative success of the secular parties may be a sign that a significant number of Iraqis are disillusioned with the religious parties that have been in power but have done little to deliver needed services. Well-known incumbent parties also did well.

The Americans had pushed for the provincial elections as a way to redistribute power more evenly throughout the country after many Iraqis boycotted the last elections in 2005. It was unclear whether a lower-than-expected turnout, at 51 percent nationwide, would curb hopes that all Iraqi sectarian and ethnic groups could be more accurately represented.

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A woman voted in Baghdad.Credit
Johan Spanner for The New York Times

Faraj al-Haideri, the head of the Independent High Electoral Commission, described the election as fair and said there was no evidence of major fraud. He said the commission was “very pleased with the turnout,” adding, “Very rarely in other parts of the world do you get such a high percentage voting in provincial elections.”

Low turnout of just 40 percent in Anbar Province was a particular surprise because the area, for years racked by a brutal insurgency, is now relatively calm and many people were eager to vote after having sat out the elections in 2005. Despite the low numbers in Anbar, the electoral commission said Sunni participation nationwide was higher than it had been in 2005.

The turnout appeared to reflect confusion over voting procedures as well as voter apathy. There were complaints across the country from Iraqis who had tried to vote but were unable to do so. Most were prevented either because a strict curfew prevented them from reaching their polling center or because their names were not on the center’s voter roll when they got there.

Part of the problem was caused by the large number of internally displaced Iraqis who no longer live in the province where they are registered to vote. About one million Iraqis were displaced as a result of sectarian and ethnic fighting over the past five years, and while some have returned the majority are living outside their home province.

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Prime Minister Nuri Kamal al-Maliki greeted a cleric at a pre-election rally. Mr. Malikis Dawa Party had strong gains in preliminary returns.Credit
Johan Spanner for The New York Times

It was too early to tell whether those people who were unable to vote would seek redress or resort to violence — or simply resign themselves to not having a voice.

Most parties said they were not planning to contest the results, at least for now, though a few, including the Iraqi Front for National Dialogue, said they had not ruled it out.

While official results of how many seats each party won are still several days off, interviews with election officials in a number of provinces as well as independent observers and representatives of political parties indicated that Mr. Maliki’s Dawa Party gained electoral support in most provinces. The party’s television channel said it had won in Baghdad and Basra.

However, that seemed to mean that the party received more votes than other parties but not necessarily a majority.

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Voting booths on Saturday in the Sunni district of Adhamiya in Baghdad, where early voting was light. Credit
Alaa al-Marjani/Associated Press

The Dawa Party’s claim was corroborated by its strongest competitor in the south, the Islamic Supreme Council of Iraq, which previously controlled Baghdad. Its television network said it had not won Baghdad or Basra.

Maithem Hussein, the head of an nongovernment organization tracking the election in Basra, said Mr. Maliki’s victory there was expected. “Maliki has saved Basra from militias,” he said. “Basra owes him.”

Although the Supreme Council, which relied on its Shiite religious identity during the campaign, lost seats in several provinces, it was still among the top three or four vote-getters in most provinces south of Baghdad.

Other incumbent parties also had strong showings in multiple provinces, including the secular Iraqi National List led by Ayad Allawi, a former interim prime minister; the Iraqi Islamic Party led by Vice President Tariq al-Hashimi, a Sunni; and the nominally independent parties backed by the Shiite cleric Moktada al-Sadr.

Several politicians said the strong showing by Mr. Allawi’s party was notable. “This really reflects that Iraqi society is looking for alternatives — they do not necessarily believe that the Islamists should lead the country,” said Qassim Daoud, a member of Parliament and one of the leaders of an independent, secular-leaning party. “The public are interested in services, and this election has shown them that they can change anything by democratic means if they are not satisfied.”

Members of another independent party, the National Reformation Movement, expressed similar views. “At least we will get some seats and we will make alliances with other blocs,” said Moad al-Obaidi, a party member.

Some party officials blamed the electoral commission for failing to make the registration system simpler. The commission defended its procedure and said it was a trade-off between a completely accessible system and one with integrity, said Ayad Hillal al-Kinani, a commission member. He said people had 45 days to change their registration. An effort was made to direct people to the correct voting center by posting signs near the offices of local food-ration agents explaining the location of voting centers. All Iraqis receive a basket of monthly food rations, a holdover from the era of Saddam Hussein.

Frustrated with the government and disillusioned with its performance over the past four years, a number of people appeared to have decided to skip voting altogether. “I did not vote because I could not find a qualified candidate that I can trust — all those candidates came for their personal benefits,” said Maher Naji, 37, a day laborer in Falluja.

The Falluja area of Anbar Province had one of the lowest turnouts in the country, with some estimates that only 25 percent of eligible voters went to the polls. Over all, the province had extremely low turnout and the new tribal parties that believed they would do well were furious that their main competitor, the religious Iraqi Islamic Party, appeared to have once again won a large number of seats.

Ahmed Abu Risha, a powerful tribesman in Anbar Province and the brother of one of the founders of the Awakening councils, which joined the Americans to fight Islamic insurgents, said he believed that the turnout was lower than the 40 percent announced by the election commission and that the numbers were being manipulated by the Iraqi Islamic Party. “If the Islamic Party wins, it will be another Darfur,” he said.

Reporting was contributed by Sam Dagher, Timothy Williams, Atheer Kakan, Suadad al-Salhy and Mohamed Hussein from Baghdad, and Iraqi employees of The New York Times from Nineveh, Anbar, Babil, Najaf and Diyala Provinces.

A version of this article appears in print on , on Page A1 of the New York edition with the headline: Secular Parties And Premier Ahead in Iraq. Order Reprints|Today's Paper|Subscribe